[
  {
    "position": 1,
    "index": 598,
    "lambda": "1",
    "list": 1,
    "formula": "1/(a**2 - 2*b**2 - 2*c**2)",
    "rational": true,
    "source": "https://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X598",
    "method": "Barycentrics first-coordinate conversion",
    "sharp_outward_centroidal_ray": true,
    "status": "Proved attractive",
    "certificate": "refined/entry_8.json",
    "group": "previous-current-base",
    "label": "F(1,X598)",
    "merge_position": 1,
    "current_base_position": 1,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 3,
    "index": 4193,
    "lambda": "1",
    "list": 1,
    "formula": "(a - b - c)*(a*b**2 - a*b*c + a*c**2 + b**3 - b**2*c - b*c**2 + c**3)",
    "rational": true,
    "source": "https://faculty.evansville.edu/ck6/encyclopedia/ETCPart3.html#X4193",
    "method": "supplied prior formula",
    "sharp_outward_centroidal_ray": true,
    "status": "Proved attractive",
    "certificate": "proofs/entry_15.json",
    "group": "previous-current-base",
    "label": "F(1,X4193)",
    "merge_position": 2,
    "current_base_position": 2,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 4,
    "index": 10523,
    "lambda": "1",
    "list": 1,
    "formula": "a**5*b**2 + a**5*c**2 - a**4*b**3 - a**4*b**2*c - a**4*b*c**2 - a**4*c**3 - 2*a**3*b**4 + 2*a**3*b**3*c + 4*a**3*b**2*c**2 + 2*a**3*b*c**3 - 2*a**3*c**4 + 2*a**2*b**5 - 2*a**2*b**3*c**2 - 2*a**2*b**2*c**3 + 2*a**2*c**5 + a*b**6 - 2*a*b**5*c - a*b**4*c**2 + 4*a*b**3*c**3 - a*b**2*c**4 - 2*a*b*c**5 + a*c**6 - b**7 + b**6*c + 3*b**5*c**2 - 3*b**4*c**3 - 3*b**3*c**4 + 3*b**2*c**5 + b*c**6 - c**7",
    "rational": true,
    "source": "https://faculty.evansville.edu/ck6/encyclopedia/ETCPart6.html#X10523",
    "method": "supplied prior formula",
    "sharp_outward_centroidal_ray": true,
    "status": "Proved attractive",
    "certificate": "proofs/entry_20.json",
    "group": "previous-current-base",
    "label": "F(1,X10523)",
    "merge_position": 3,
    "current_base_position": 3,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 6,
    "index": 12877,
    "lambda": "1",
    "list": 1,
    "formula": "(-a + b + c)*(3*a**6 - a**4*(5*b**2 + 5*c**2) - 4*a**3*b*c*(b + c) + a**2*(b**4 - b*c*(2*b**2 - b*c + 2*c**2) + c**4) + (b - c)**2*(b**2 - c**2)**2)",
    "rational": true,
    "source": "https://faculty.evansville.edu/ck6/encyclopedia/ETCPart7.html#X12877",
    "method": "Barycentrics first-coordinate conversion",
    "sharp_outward_centroidal_ray": true,
    "status": "Proved attractive",
    "certificate": "proofs/entry_38.json",
    "group": "previous-current-base",
    "label": "F(1,X12877)",
    "merge_position": 4,
    "current_base_position": 4,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 7,
    "index": 15518,
    "lambda": "1",
    "list": 1,
    "formula": "a*(a**8 - 2*a**7*b - 2*a**7*c - 2*a**6*b**2 + 4*a**6*b*c - 2*a**6*c**2 + 6*a**5*b**3 + 2*a**5*b**2*c + 2*a**5*b*c**2 + 6*a**5*c**3 - 8*a**4*b**3*c - 4*a**4*b**2*c**2 - 8*a**4*b*c**3 - 6*a**3*b**5 + 2*a**3*b**4*c + 12*a**3*b**3*c**2 + 12*a**3*b**2*c**3 + 2*a**3*b*c**4 - 6*a**3*c**5 + 2*a**2*b**6 + 4*a**2*b**5*c - 6*a**2*b**4*c**2 - 6*a**2*b**2*c**4 + 4*a**2*b*c**5 + 2*a**2*c**6 + 2*a*b**7 - 2*a*b**6*c - 6*a*b**5*c**2 + 6*a*b**4*c**3 + 6*a*b**3*c**4 - 6*a*b**2*c**5 - 2*a*b*c**6 + 2*a*c**7 - b**8 + 4*b**6*c**2 - 6*b**4*c**4 + 4*b**2*c**6 - c**8)",
    "rational": true,
    "source": "https://faculty.evansville.edu/ck6/encyclopedia/ETCPart8.html#X15518",
    "method": "supplied prior formula",
    "sharp_outward_centroidal_ray": true,
    "status": "Proved attractive",
    "certificate": "proofs/entry_48.json",
    "group": "previous-current-base",
    "label": "F(1,X15518)",
    "merge_position": 5,
    "current_base_position": 5,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 10,
    "index": 19678,
    "lambda": "1",
    "list": 2,
    "formula": "a**6*b + a**6*c + a**5*b**2 + a**5*c**2 + a**4*b**2*c + a**4*b*c**2 - a**3*b**3*c - a**3*b*c**3 + a**2*b**3*c**2 + a**2*b**2*c**3 - a*b**5*c + a*b**4*c**2 + a*b**2*c**4 - a*b*c**5 + b**4*c**3 + b**3*c**4",
    "rational": true,
    "source": "https://faculty.evansville.edu/ck6/encyclopedia/ETCPart10.html#X19678",
    "method": "Barycentrics first-coordinate conversion",
    "sharp_outward_centroidal_ray": false,
    "status": "Proved attractive",
    "certificate": "proofs/entry_71.json",
    "group": "previous-current-base",
    "label": "F(1,X19678)",
    "merge_position": 6,
    "current_base_position": 6,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 12,
    "index": 27277,
    "lambda": "1",
    "list": 2,
    "formula": "a**8*b + a**8*c + a**7*b**2 + a**7*b*c + a**7*c**2 - a**6*b**3 - 3*a**6*b**2*c - 3*a**6*b*c**2 - a**6*c**3 - a**5*b**4 - 3*a**5*b**3*c - 5*a**5*b**2*c**2 - 3*a**5*b*c**3 - a**5*c**4 - a**4*b**5 + 7*a**4*b**3*c**2 + 7*a**4*b**2*c**3 - a**4*c**5 - a**3*b**6 - a**3*b**5*c + 7*a**3*b**4*c**2 + 14*a**3*b**3*c**3 + 7*a**3*b**2*c**4 - a**3*b*c**5 - a**3*c**6 + a**2*b**7 + a**2*b**6*c - a**2*b**5*c**2 + 3*a**2*b**4*c**3 + 3*a**2*b**3*c**4 - a**2*b**2*c**5 + a**2*b*c**6 + a**2*c**7 + a*b**8 + 3*a*b**7*c + a*b**6*c**2 - 3*a*b**5*c**3 - 4*a*b**4*c**4 - 3*a*b**3*c**5 + a*b**2*c**6 + 3*a*b*c**7 + a*c**8 + b**8*c + b**7*c**2 - b**6*c**3 - b**5*c**4 - b**4*c**5 - b**3*c**6 + b**2*c**7 + b*c**8",
    "rational": true,
    "source": "supplied candidate38-first-pass.json",
    "method": "supplied prior formula",
    "sharp_outward_centroidal_ray": false,
    "status": "Proved attractive",
    "certificate": "proofs/entry_80.json",
    "group": "previous-current-base",
    "label": "F(1,X27277)",
    "merge_position": 7,
    "current_base_position": 7,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 13,
    "index": 27328,
    "lambda": "1",
    "list": 2,
    "formula": "a**8*b + a**8*c + a**7*b**2 + 3*a**7*b*c + a**7*c**2 - a**6*b**3 + 3*a**6*b**2*c + 3*a**6*b*c**2 - a**6*c**3 - a**5*b**4 - a**5*b**3*c + a**5*b**2*c**2 - a**5*b*c**3 - a**5*c**4 - a**4*b**5 - 4*a**4*b**4*c + 3*a**4*b**3*c**2 + 3*a**4*b**2*c**3 - 4*a**4*b*c**4 - a**4*c**5 - a**3*b**6 - 3*a**3*b**5*c + 3*a**3*b**4*c**2 + 10*a**3*b**3*c**3 + 3*a**3*b**2*c**4 - 3*a**3*b*c**5 - a**3*c**6 + a**2*b**7 - a**2*b**6*c - 3*a**2*b**5*c**2 + 7*a**2*b**4*c**3 + 7*a**2*b**3*c**4 - 3*a**2*b**2*c**5 - a**2*b*c**6 + a**2*c**7 + a*b**8 + a*b**7*c - a*b**6*c**2 - a*b**5*c**3 - a*b**3*c**5 - a*b**2*c**6 + a*b*c**7 + a*c**8 + b**8*c + b**7*c**2 - b**6*c**3 - b**5*c**4 - b**4*c**5 - b**3*c**6 + b**2*c**7 + b*c**8",
    "rational": true,
    "source": "supplied candidate38-first-pass.json",
    "method": "supplied prior formula",
    "sharp_outward_centroidal_ray": false,
    "status": "Proved attractive",
    "certificate": "proofs/entry_82.json",
    "group": "previous-current-base",
    "label": "F(1,X27328)",
    "merge_position": 8,
    "current_base_position": 8,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 14,
    "index": 37828,
    "lambda": "1",
    "list": 2,
    "formula": "a**4 + a**3*b + a**3*c - 2*a**2*b**2 - 2*a**2*b*c - 2*a**2*c**2 - a*b**3 + 3*a*b**2*c + 3*a*b*c**2 - a*c**3 + b**4 - 2*b**2*c**2 + c**4",
    "rational": true,
    "source": "supplied candidate38-first-pass.json",
    "method": "supplied prior formula",
    "sharp_outward_centroidal_ray": true,
    "status": "Proved attractive",
    "certificate": "proofs/entry_86.json",
    "group": "previous-current-base",
    "label": "F(1,X37828)",
    "merge_position": 9,
    "current_base_position": 9,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 15,
    "index": 39141,
    "lambda": "1",
    "list": 2,
    "formula": "2*a**6 - a**4*b**2 - a**4*c**2 + a**2*b**4 - a**2*b**2*c**2 + a**2*c**4 + b**4*c**2 + b**2*c**4",
    "rational": true,
    "source": "https://faculty.evansville.edu/ck6/encyclopedia/ETCPart20.html#X39141",
    "method": "supplied prior formula",
    "sharp_outward_centroidal_ray": false,
    "status": "Proved attractive",
    "certificate": "proofs/entry_87.json",
    "group": "previous-current-base",
    "label": "F(1,X39141)",
    "merge_position": 10,
    "current_base_position": 10,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 17,
    "index": 59544,
    "lambda": "1",
    "list": 2,
    "formula": "4*a**3 - a**2*(b + c) - 2*a*(b**2 + c**2) + (b + c)*(b**2 + c**2)",
    "rational": true,
    "source": "https://faculty.evansville.edu/ck6/encyclopedia/ETCPart30.html#X59544",
    "method": "supplied prior formula",
    "sharp_outward_centroidal_ray": true,
    "status": "Proved attractive",
    "certificate": "proofs/entry_89.json",
    "group": "previous-current-base",
    "label": "F(1,X59544)",
    "merge_position": 11,
    "current_base_position": 11,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 18,
    "index": 59572,
    "lambda": "1",
    "list": 2,
    "formula": "3*a**3 - 3*a**2*(b + c) - a*(b**2 - 6*b*c + c**2) + (b - c)**2*(b + c)",
    "rational": true,
    "source": "https://faculty.evansville.edu/ck6/encyclopedia/ETCPart30.html#X59572",
    "method": "supplied prior formula",
    "sharp_outward_centroidal_ray": true,
    "status": "Proved attractive",
    "certificate": "proofs/entry_90.json",
    "group": "previous-current-base",
    "label": "F(1,X59572)",
    "merge_position": 12,
    "current_base_position": 12,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 19,
    "index": 59639,
    "lambda": "1",
    "list": 2,
    "formula": "2*a**4 + 3*a**3*(b + c) - a**2*(b + c)**2 - a*(b + c)**3 + (b + c)**2*(b**2 + c**2)",
    "rational": true,
    "source": "https://faculty.evansville.edu/ck6/encyclopedia/ETCPart30.html#X59639",
    "method": "supplied prior formula",
    "sharp_outward_centroidal_ray": true,
    "status": "Proved attractive",
    "certificate": "proofs/entry_91.json",
    "group": "previous-current-base",
    "label": "F(1,X59639)",
    "merge_position": 13,
    "current_base_position": 13,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 20,
    "index": 66632,
    "lambda": "1",
    "list": 2,
    "formula": "2*a**3 - a**2*(b + c) + 2*a*b*c + (b - c)**2*(b + c)",
    "rational": true,
    "source": "https://faculty.evansville.edu/ck6/encyclopedia/ETCPart34.html#X66632",
    "method": "supplied prior formula",
    "sharp_outward_centroidal_ray": true,
    "status": "Proved attractive",
    "certificate": "proofs/entry_92.json",
    "group": "previous-current-base",
    "label": "F(1,X66632)",
    "merge_position": 14,
    "current_base_position": 14,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 24,
    "index": 345,
    "endpoint": "Lambda2",
    "lambda": "1/7",
    "formula": "(a - b - c)*(a**2 - b**2 - c**2)",
    "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
    "numerical_lambda": "0.14285714286",
    "historical_record": {
      "Index": 345,
      "ETCFunction": "(a - b - c)*(a^2 - b^2 - c^2)"
    },
    "rational": true,
    "group": "previous-current-base",
    "label": "F(1/7,X345)",
    "merge_position": 15,
    "current_base_position": 15,
    "necessity_status": "proved necessary in B41"
  },
  {
    "index": 58,
    "lambda": "2/3",
    "formula": "a**2*(a + b)*(a + c)",
    "group": "previous-current-base",
    "rational": true,
    "position": 29,
    "label": "F(2/3,X58)",
    "source": "Preserved first150 historical formula; exact endpoint endorsed by new handoff",
    "merge_position": 16,
    "current_base_position": 16,
    "necessity_status": "proved necessary in B41"
  },
  {
    "index": 1476,
    "lambda": "-1/2",
    "formula": "a/((a - b - c)*((b - c)^2 + a*(b + c)))",
    "rational": true,
    "label": "F(-1/2,X1476)",
    "group": "previous-current-base",
    "source": "X1001-X2000 verified handoff",
    "merge_position": 17,
    "current_base_position": 17,
    "necessity_status": "not proved necessary; retained for proved sufficiency"
  },
  {
    "position": 4,
    "index": 2093,
    "endpoint": "Lambda1",
    "lambda": "-2/7",
    "formula": "a*(a**3 + 3*a**2*(b + c) - a*(b + c)**2 - 3*(b - c)**2*(b + c))",
    "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
    "numerical_lambda": "-0.28571428571",
    "historical_record": {
      "Index": 2093,
      "ETCFunction": "a*(a^3 + 3*a^2*(b + c) - 3*(b - c)^2*(b + c) - a*(b + c)^2)"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 18,
    "label": "F(-2/7,X2093)",
    "current_base_position": 18,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 11,
    "index": 2255,
    "endpoint": "Lambda1",
    "lambda": "-1/3",
    "formula": "a**2/(a**3 - a**2*(b + c) - a*(b - c)**2 + (b + c)**3)",
    "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
    "numerical_lambda": "-0.33333333333",
    "historical_record": {
      "Index": 2255,
      "ETCFunction": "a^2/(a^3 - a*(b - c)^2 - a^2*(b + c) + (b + c)^3)"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 19,
    "label": "F(-1/3,X2255)",
    "current_base_position": 19,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 51,
    "index": 3501,
    "endpoint": "Lambda2",
    "lambda": "1",
    "formula": "a*(a**2*b + a**2*c - a*b**2 - a*b*c - a*c**2 + b**2*c + b*c**2)",
    "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
    "numerical_lambda": "1.0",
    "historical_record": {
      "Index": 3501,
      "ETCFunction": "a*(a^2*b - a*b^2 + a^2*c - a*b*c + b^2*c - a*c^2 + b*c^2)"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 20,
    "label": "F(1,X3501)",
    "current_base_position": 20,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 164,
    "index": 3794,
    "endpoint": "Lambda2",
    "lambda": "1",
    "formula": "a*(a + b)*(a + c)*(a - b - c)*(b**2 - b*c + c**2)",
    "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
    "numerical_lambda": "1.0",
    "historical_record": {
      "Index": 3794,
      "ETCFunction": "a*(a + b)*(a - b - c)*(a + c)*(b^2 - b*c + c^2)"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 21,
    "label": "F(1,X3794)",
    "current_base_position": 21,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 171,
    "index": 3825,
    "endpoint": "Lambda2",
    "lambda": "8/5",
    "formula": "-a**2*b**2 + 2*a**2*b*c - a**2*c**2 + a*b**2*c + a*b*c**2 + b**4 - 2*b**2*c**2 + c**4",
    "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
    "numerical_lambda": "1.6",
    "historical_record": {
      "Index": 3825,
      "ETCFunction": "-(a^2*b^2) + b^4 + 2*a^2*b*c + a*b^2*c - a^2*c^2 + a*b*c^2 - 2*b^2*c^2 + c^4"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 22,
    "label": "F(8/5,X3825)",
    "current_base_position": 22,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 221,
    "index": 3951,
    "endpoint": "Lambda1",
    "lambda": "-1/2",
    "formula": "a*(a + 3*b + 3*c)*(a**2 - b**2 - c**2)",
    "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
    "numerical_lambda": "-0.5",
    "historical_record": {
      "Index": 3951,
      "ETCFunction": "a*(a + 3*b + 3*c)*(a^2 - b^2 - c^2)"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 23,
    "label": "F(-1/2,X3951)",
    "current_base_position": 23,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 239,
    "index": 4012,
    "endpoint": "Lambda2",
    "lambda": "1/4",
    "formula": "(a - b - c)**3*(a**2 + b**2 - 2*b*c + c**2)",
    "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
    "numerical_lambda": "0.25",
    "historical_record": {
      "Index": 4012,
      "ETCFunction": "(a - b - c)^3*(a^2 + b^2 - 2*b*c + c^2)"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 24,
    "label": "F(1/4,X4012)",
    "current_base_position": 24,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 316,
    "index": 4308,
    "endpoint": "Lambda1",
    "lambda": "-1/2",
    "formula": "(a - b + c)*(a + b - c)*(5*a**2 - 2*a*b - 2*a*c + b**2 + 2*b*c + c**2)",
    "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
    "numerical_lambda": "-0.5",
    "historical_record": {
      "Index": 4308,
      "ETCFunction": "(a + b - c)*(a - b + c)*(5*a^2 - 2*a*b + b^2 - 2*a*c + 2*b*c + c^2)"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 25,
    "label": "F(-1/2,X4308)",
    "current_base_position": 25,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 328,
    "index": 4321,
    "endpoint": "Lambda1",
    "lambda": "-1/2",
    "formula": "a*(a - b + c)*(a + b - c)*(a**3 - 3*a**2*b - 3*a**2*c + 3*a*b**2 - 2*a*b*c + 3*a*c**2 - b**3 - 3*b**2*c - 3*b*c**2 - c**3)",
    "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
    "numerical_lambda": "-0.5",
    "historical_record": {
      "Index": 4321,
      "ETCFunction": "a*(a + b - c)*(a - b + c)*(a^3 - 3*a^2*b + 3*a*b^2 - b^3 - 3*a^2*c - 2*a*b*c - 3*b^2*c + 3*a*c^2 - 3*b*c^2 - c^3)"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 26,
    "label": "F(-1/2,X4321)",
    "current_base_position": 26,
    "necessity_status": "not proved necessary; retained for proved sufficiency"
  },
  {
    "position": 344,
    "index": 4342,
    "endpoint": "Lambda2",
    "lambda": "1",
    "formula": "(a - b - c)*(3*a**2*b + 3*a**2*c + 4*a*b**2 - 8*a*b*c + 4*a*c**2 + b**3 - b**2*c - b*c**2 + c**3)",
    "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
    "numerical_lambda": "1.0",
    "historical_record": {
      "Index": 4342,
      "ETCFunction": "(a - b - c)*(3*a^2*b + 4*a*b^2 + b^3 + 3*a^2*c - 8*a*b*c - b^2*c + 4*a*c^2 - b*c^2 + c^3)"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 27,
    "label": "F(1,X4342)",
    "current_base_position": 27,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 378,
    "index": 4438,
    "endpoint": "Lambda1",
    "lambda": "-2",
    "formula": "a**3 - a*b**2 - a*c**2 + b**3 + c**3",
    "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
    "numerical_lambda": "-2.0",
    "historical_record": {
      "Index": 4438,
      "ETCFunction": "a^3 - a*b^2 + b^3 - a*c^2 + c^3"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 28,
    "label": "F(-2,X4438)",
    "current_base_position": 28,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 459,
    "index": 4857,
    "endpoint": "Lambda2",
    "lambda": "2/3",
    "formula": "-a**4 + 3*a**2*b*c + b**4 - 2*b**2*c**2 + c**4",
    "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
    "numerical_lambda": "0.66666666667",
    "historical_record": {
      "Index": 4857,
      "ETCFunction": "-a^4 + b^4 + 3*a^2*b*c - 2*b^2*c^2 + c^4"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 29,
    "label": "F(2/3,X4857)",
    "current_base_position": 29,
    "necessity_status": "not proved necessary; retained for proved sufficiency"
  },
  {
    "position": 479,
    "index": 4911,
    "endpoint": "Lambda2",
    "lambda": "2/5",
    "formula": "a**4 + a**2*b*c - b**4 + b**3*c + b*c**3 - c**4",
    "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
    "numerical_lambda": "0.40000000831",
    "historical_record": {
      "Index": 4911,
      "ETCFunction": "a^4 - b^4 + a^2*b*c + b^3*c + b*c^3 - c^4"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 30,
    "label": "F(2/5,X4911)",
    "current_base_position": 30,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 77,
    "index": 5255,
    "endpoint": "Lambda2",
    "lambda": "1",
    "formula": "a*(a**3 + a**2*b + a**2*c - a*b*c + b**2*c + b*c**2)",
    "source": "ETC_X1_X72807.wxf; SHA256 ACE501D40DD83785F89B4DE8E4DDCC0C5081D82DE82E1BAF37816D10E547CBFA; S=twice area",
    "numerical_lambda": "1.0",
    "historical_record": {
      "Index": 5255,
      "ETCFunction": "a*(a^3 + a^2*b + a^2*c - a*b*c + b^2*c + b*c^2)"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 31,
    "label": "F(1,X5255)",
    "current_base_position": 31,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 98,
    "index": 5310,
    "endpoint": "Lambda1",
    "lambda": "-1/4",
    "formula": "a**2*(a**4 - a**2*b*c - b**4 - b**3*c - b*c**3 - c**4)",
    "source": "ETC_X1_X72807.wxf; SHA256 ACE501D40DD83785F89B4DE8E4DDCC0C5081D82DE82E1BAF37816D10E547CBFA; S=twice area",
    "numerical_lambda": "-0.25",
    "historical_record": {
      "Index": 5310,
      "ETCFunction": "a^2*(a^4 - b^4 - a^2*b*c - b^3*c - b*c^3 - c^4)"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 32,
    "label": "F(-1/4,X5310)",
    "current_base_position": 32,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 185,
    "index": 5741,
    "endpoint": "Lambda1",
    "lambda": "-1/2",
    "formula": "-a**2*b - a**2*c + 2*a*b*c + b**3 + c**3",
    "source": "ETC_X1_X72807.wxf; SHA256 ACE501D40DD83785F89B4DE8E4DDCC0C5081D82DE82E1BAF37816D10E547CBFA; S=twice area",
    "numerical_lambda": "-0.5",
    "historical_record": {
      "Index": 5741,
      "ETCFunction": "-(a^2*b) + b^3 - a^2*c + 2*a*b*c + c^3"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 33,
    "label": "F(-1/2,X5741)",
    "current_base_position": 33,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 244,
    "index": 6205,
    "endpoint": "Lambda1",
    "lambda": "-1/2",
    "formula": "a*(a**3 + 2*a**2*b + 2*a**2*c - 2*a*b**2 - 2*a*c**2 - b**3 + 2*b**2*c + 2*b*c**2 - c**3)",
    "source": "ETC_X1_X72807.wxf; SHA256 ACE501D40DD83785F89B4DE8E4DDCC0C5081D82DE82E1BAF37816D10E547CBFA; S=twice area",
    "numerical_lambda": "-0.5",
    "historical_record": {
      "Index": 6205,
      "ETCFunction": "a*(a^3 + 2*a^2*b - 2*a*b^2 - b^3 + 2*a^2*c + 2*b^2*c - 2*a*c^2 + 2*b*c^2 - c^3)"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 34,
    "label": "F(-1/2,X6205)",
    "current_base_position": 34,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 378,
    "index": 7748,
    "endpoint": "Lambda2",
    "lambda": "3/7",
    "formula": "-a**4 + a**2*b**2 + a**2*c**2 + b**4 - 2*b**2*c**2 + c**4",
    "source": "ETC_X1_X72807.wxf; SHA256 ACE501D40DD83785F89B4DE8E4DDCC0C5081D82DE82E1BAF37816D10E547CBFA; S=twice area",
    "numerical_lambda": "0.42857142857",
    "historical_record": {
      "Index": 7748,
      "ETCFunction": "-a^4 + a^2*b^2 + b^4 + a^2*c^2 - 2*b^2*c^2 + c^4"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 35,
    "label": "F(3/7,X7748)",
    "current_base_position": 35,
    "necessity_status": "not proved necessary; retained for proved sufficiency"
  },
  {
    "position": 457,
    "index": 7872,
    "endpoint": "Lambda1",
    "lambda": "-4/3",
    "formula": "-a**4 + 2*a**2*b**2 + 2*a**2*c**2 + 2*b**4 - 2*b**2*c**2 + 2*c**4",
    "source": "ETC_X1_X72807.wxf; SHA256 ACE501D40DD83785F89B4DE8E4DDCC0C5081D82DE82E1BAF37816D10E547CBFA; S=twice area",
    "numerical_lambda": "-1.3333333333",
    "historical_record": {
      "Index": 7872,
      "ETCFunction": "-a^4 + 2*a^2*b^2 + 2*b^4 + 2*a^2*c^2 - 2*b^2*c^2 + 2*c^4"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 36,
    "label": "F(-4/3,X7872)",
    "current_base_position": 36,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 618,
    "index": 9597,
    "endpoint": "Lambda2",
    "lambda": "5/11",
    "formula": "-a**4 + 2*a**2*b**2 - 2*a**2*b*c + 2*a**2*c**2 + b**4 - 2*b**2*c**2 + c**4",
    "source": "ETC_X1_X72807.wxf; SHA256 ACE501D40DD83785F89B4DE8E4DDCC0C5081D82DE82E1BAF37816D10E547CBFA; S=twice area",
    "numerical_lambda": "0.45454545455",
    "historical_record": {
      "Index": 9597,
      "ETCFunction": "-a^4 + 2*a^2*b^2 + b^4 - 2*a^2*b*c + 2*a^2*c^2 - 2*b^2*c^2 + c^4"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 37,
    "label": "F(5/11,X9597)",
    "current_base_position": 37,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 671,
    "index": 10000,
    "endpoint": "Lambda1",
    "lambda": "-3/2",
    "formula": "a**8 + a**4*b**4 + a**4*b**2*c**2 + a**4*c**4 + a**2*b**4*c**2 + a**2*b**2*c**4 + b**6*c**2 + b**4*c**4 + b**2*c**6",
    "source": "ETC_X1_X72807.wxf; SHA256 ACE501D40DD83785F89B4DE8E4DDCC0C5081D82DE82E1BAF37816D10E547CBFA; S=twice area",
    "numerical_lambda": "-1.5",
    "historical_record": {
      "Index": 10000,
      "ETCFunction": "a^8 + a^4*b^4 + a^4*b^2*c^2 + a^2*b^4*c^2 + b^6*c^2 + a^4*c^4 + a^2*b^2*c^4 + b^4*c^4 + b^2*c^6"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 38,
    "label": "F(-3/2,X10000)",
    "current_base_position": 38,
    "necessity_status": "not proved necessary; retained for proved sufficiency"
  },
  {
    "position": 672,
    "index": 10000,
    "endpoint": "Lambda2",
    "lambda": "7/6",
    "formula": "a**8 + a**4*b**4 + a**4*b**2*c**2 + a**4*c**4 + a**2*b**4*c**2 + a**2*b**2*c**4 + b**6*c**2 + b**4*c**4 + b**2*c**6",
    "source": "ETC_X1_X72807.wxf; SHA256 ACE501D40DD83785F89B4DE8E4DDCC0C5081D82DE82E1BAF37816D10E547CBFA; S=twice area",
    "numerical_lambda": "1.1666666667",
    "historical_record": {
      "Index": 10000,
      "ETCFunction": "a^8 + a^4*b^4 + a^4*b^2*c^2 + a^2*b^4*c^2 + b^6*c^2 + a^4*c^4 + a^2*b^2*c^4 + b^4*c^4 + b^2*c^6"
    },
    "rational": true,
    "group": "previous-current-base",
    "merge_position": 39,
    "label": "F(7/6,X10000)",
    "current_base_position": 39,
    "necessity_status": "proved necessary in B41"
  },
  {
    "position": 594,
    "index": 9445,
    "endpoint": "Lambda1",
    "lambda": "-1/2",
    "formula": "a*(a**3*b - 2*a**2*b**2 - a**2*c**2 + a*b**3 - 3*a*b*c**2 + 2*a*c**3 - b**2*c**2 + 2*b*c**3 - c**4)*(a**3*c - a**2*b**2 - 2*a**2*c**2 + 2*a*b**3 - 3*a*b**2*c + a*c**3 - b**4 + 2*b**3*c - b**2*c**2)",
    "source": "ETC_X1_X72807.wxf; SHA256 ACE501D40DD83785F89B4DE8E4DDCC0C5081D82DE82E1BAF37816D10E547CBFA; S=twice area",
    "numerical_lambda": "-0.5",
    "historical_record": {
      "Index": 9445,
      "ETCFunction": "a*(-(a^2*b^2) + 2*a*b^3 - b^4 + a^3*c - 3*a*b^2*c + 2*b^3*c - 2*a^2*c^2 - b^2*c^2 + a*c^3)*(a^3*b - 2*a^2*b^2 + a*b^3 - a^2*c^2 - 3*a*b*c^2 - b^2*c^2 + 2*a*c^3 + 2*b*c^3 - c^4)"
    },
    "rational": true,
    "group": "X5001-X10000 unresolved-required-for-proof",
    "merge_position": 40,
    "label": "F(-1/2,X9445)",
    "current_base_position": 40,
    "necessity_status": "not proved necessary; retained for proved sufficiency"
  },
  {
    "position": 595,
    "index": 9446,
    "endpoint": "Lambda1",
    "lambda": "-1/2",
    "formula": "(a - b + c)*(a + b - c)*(a**4 - 2*a**3*b - 2*a**3*c + a**2*b**2 + 3*a**2*b*c + a**2*c**2 - b**3*c + 2*b**2*c**2 - b*c**3)",
    "source": "ETC_X1_X72807.wxf; SHA256 ACE501D40DD83785F89B4DE8E4DDCC0C5081D82DE82E1BAF37816D10E547CBFA; S=twice area",
    "numerical_lambda": "-0.5",
    "historical_record": {
      "Index": 9446,
      "ETCFunction": "(a + b - c)*(a - b + c)*(a^4 - 2*a^3*b + a^2*b^2 - 2*a^3*c + 3*a^2*b*c - b^3*c + a^2*c^2 + 2*b^2*c^2 - b*c^3)"
    },
    "rational": true,
    "group": "X5001-X10000 unresolved-required-for-proof",
    "merge_position": 41,
    "label": "F(-1/2,X9446)",
    "current_base_position": 41,
    "necessity_status": "not proved necessary; retained for proved sufficiency"
  }
]